Try to download in pdf format if the below is not clear
Code No: R05010102 Set No. 1
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICS-I
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering, Aeronautical Engineering, Instrumentation & Control
Engineering and Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1.(a) Test the convergence of the series 2/1 + 2.5.8/1.5.9 + 2.5.8.11/1.5−9.13 +...O<
b) Find whether the following series converges absolutely / condtionally
1/6 − 1/6 . 1/3 + 1.3.5/6.8.10 −1.3.5.7/6.8.10.12 .
(c) Prove that pi/6 +
p3
5 < sin−1 3
5 < π/6 + 1
8 . [6]
2. (a) Show that the functions u = x+y+z , v = x2+y2+z2-2xy-2zx-2yz and
w = x3+y3+z3-3xyz are functionally related. Find the relation between them.
(b) Find the centre of curvature at the point a
4 , a
4 of the curve px +py = pa.
Find also the equation of the circle of curvature at that point. [8+8]
3. (a) Find the length of the curve x2(a2 – x2) = 8 a2y2.
(b) Find the volume of the solid generated by revolving the lemniscates r2 = a2
Cos 2θ about the line θ =
2 . [8+8]
4. (a) Form the differential equation by eliminating the arbitrary constant : log y/x
= cx. [3]
(b) Solve the differential equation: ( 1+ y2) dx = ( tan −1y – x ) dy. [7]
(c) The temperature of the body drops from 1000 C to 750C in ten minutes when
the surrounding air is at 200C temperature. What will be its temperature
after half an hour. When will the temperature be 250C. [6]
5. (a) Solve the differential equation: (D2-1)y= xsinx + x2 ex.
(b) Solve the differential equation: (x2D2+xD+4)y=log x cos (2logx). [8+8]
6. (a) Prove that L [ 1
t f(t) =
1R
s
f(s) ds where L [f(t) ] = f (s) [5]
(b) Find the inverse Laplace Transformation of 3(s2
−2)2
2 s5 [6]
(c) Evaluate s s (x2 + y2)dxdy over the area bounded by the ellipse x2
a2 + y2
b2 = 1
[5]
7. (a) For any vector A, find div curl A. [6]
(b) Evaluate RR
s
A.n ds where A=z i +x j-3y2z k and S is the surface of the cylinder
x2 + y2 = 16included in the first octant between z=0 and z=5. [10]
8. Verify Stoke’s theorem for F = -y3i+x3j in the region x2+y2 < 1, z=0. [16]
Click here to download the Question paper in Pdf format
